Which would emit the lowest frequency?

Question

Which energy transition would emit a photon with the lowest frequency of light in a hydrogen-like atom?

n=2 to n=3

n=3 to n=9

n=8 to n=5

n=4 to n=2

Answer 1

a) n=2 to n=3, b) n=3 to n=9

c) n=8 to n=5, d) n=4 to n=2

When n_f < n_i a photon emitted with E_photon, so a) and b) are not the answers.

E_photon = hv = ΔΕ = - hcR_H ( 1/n_f² - 1/n_i²) hcR_H are constants

for c) ΔΕ = - hcR_H ( 1/5² - 1/8²) = - 0.0243 hcR_H

for d) ΔΕ = - hcR_H ( 1/2² - 1/4²) = - 0.1875 hcR_H

Based on E_photon = hv energy has direct relationship with frequency, lower energy has lower frequency. The answer is (c).